Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C8×#634 | C2 | semidirect |
| 5. #10589350 | C2 | semidirect |
| 6. #10589345 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 77. #634 | M16 | semidirect |
| 191. C32 | #1588 | semidirect |
| 228. C3 | #70865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#436 | 2 |
| C4×#3754 | 2 |
| C8×#634 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589350 | 2 |
| #10589345 | 2 |
| #10589320 | 2 |
| #70865 | 3 |